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Chapter 14:
Zernike Polynomials
Zernike polynomials, also known as Zernike circle polynomials, are widely used in optics. These are orthonormal polynomials over circular pupils. They were invented by Fritz Zernike (1888–1966) and his graduate student Bernard Nijboer (1915–1999). These polynomials are used extensively to represent wavefront aberrations. An aberration is a departure from perfect imaging due to the imperfections in the media or the optical system. Before the introduction of Zernike polynomials, the representation of aberrations was due to a theory developed by Philip Ludwig von Seidel (1821–1896). Seidel developed a power series expansion for the ray position, while Zernike developed a technique to decompose a wavefront into orthogonal surfaces. Zernike’s method provided a means for optimum balancing of various aberrations of an optical instrument. The reader is referred to various books for descriptions and discussion of optical aberrations.
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Zernike polynomials

Imaging systems

Optical aberrations

Optical components

Wavefront aberrations


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